Optimal ship fleet size in an inland river corridor with seasonal change in waterway depth

Inland river corridor provides a significant connection between inland cities and export seaports. Different from the sea waterway, the navigable ship size in an inland river corridor is restricted by the waterway depths in the plentiful and drought periods. This paper deals with the design issue of ship fleet size in an inland river corridor with seasonal change in waterway depth using a vertical structure model. The interactions among consignors, competitive carriers and a public port operator over plentiful and drought periods are considered in the proposed model, together with the impacts of seasonal waterway depth on the ship fleet size. The consignors aim to minimize transport cost by choosing transfer ports in each period. The competitive carriers are intended to maximize their own net profit by determining the shipping freight rates in each period and the ship fleet size (ship frequencies and composition of ship size) over a given time horizon. A public port operator, as an agent of the government, decides the port service charges in each period to maximize social welfare over the given time horizon. The effects of the ratio of drought period duration to plentiful period duration (duration ratio), the ratio of small ship size to big ship size (ship size ratio), and the actual cargo load of big ship in the drought period on the stakeholders and the system are investigated. The results show that: (i) the government always tends to subsidize the carrier at each port in the plentiful period for a large duration ratio, but to subsidize the carrier at its competitive port in the drought period for a small duration ratio and a low cargo load of a big ship at each port; and (ii) a single big (or small) ship type strategy will underestimate (or overestimate) the ship fleet size for a low cargo load of a big ship in the drought period. The method proposed in this paper can serve as a useful tool for the fleet size plan for the carriers and for port regulation for the government so as to achieve a “win-win-win” outcome among consignors, carriers and port operator.